Solving conformable fractional differential equations using Picard’s iteration method

Abstract

In this paper we will generalize Picard’s iterated approximation, to solve the conformable fractional differential equations with an initial condition. This will be by proving the uniqueness, convergence and existence of the solution under the definition and properties of the conformable fractional derivative and integral. Besides the Lipschitz condition and the Gronwall’s inequality after generalizing it to the conformable fractional case. Also, we will show some CFDE examples and their solution besides of the graphs to show the convergence of the approximation solutions to the exact one and their applications.